6. Replication


There are always two levels of replication to consider for on-farm trials. Replication within each farm and
replication between farms (and years). The purposes of these two forms are rather different. Replication
within a farm provides a (usually) rather limited level of information about the precision of the results from
that farm and also gives some protection against loss of individual plot information. Replication between
farms provides information about the overall precision of the average results over farms and also allows the
estimation of the variability of results between locations (and years).

The replication of the set of experimental treatments within sites was discussed in the report from my
previous consultancy My conclusions then remain valid. Where there is a minimum of five sites, chosen
fairly carefully to represent the variation between sites, then the use of two replicates of the set of
treatments per site is sensible, except in those experiments where the primary interest is in the variation of
effects over sites when a large number of sites is needed and within-site variation has little benefit. If fewer
than five sites are used then it is likely that the replication may need to be more than two to achieve the
necessary within-site precision.

One point that must never be forgotten is that factorial structures always provide hidden replication and
when quite large factorial structures(at least 16 treatment combinations) are being considered, as they must
be if maximum use is to be made of resources, then the insurance benefits of two explicit replicates are
much less important since even with several missing values the factorial structure permits the
reconstruction of values for all combinations.

7. Different Treatment Subsets at Different Farms

When discussing the choice of experimental treatments in section 3 we considered how a subset of the
possibly interesting treatment combinations should be selected in such a way as to give good information
about as many of the more important treatment effects as possible. Suppose we have a particular situation
where we only have room for six combinations from four two-level factors, and these must include both
(0000) and (1111). Suitable subsets would be

 (0000,0011,0101,1000,1110,1111)

or (0000,0010,0100,1011,1101,1111)

or (0000,0100,0111,1001,1010,1111)

or (0000,0011,0110,1010,1100,1111).

If the experiment is to be at a number of farms there is a choice between selecting one subset and using it at
all farms or using different subsets at different farms. Since the different subsets each provide only partial
information and the partiality varies there is clearly advantage in changing the subsets between farms so
that the combined information will be greater.

The following material from the 1989 Consultancy Report provides some additional ideas on the design
and analysis of different factorial subjects on different farms.

7.1 Some Possible Development of Designs

With the development of computers it is possible to develop designs for experiments beyond the ideas of
the 1930's which account for almost all the experimental designs used in agricultural research to-day
(thirty years after the advent of computers).